784 CHAPTER 8 Applications of Trigonometry 59. Distance between a Ship and a Lighthouse The bearing of a lighthouse from a ship was found to be N 37° E. After the ship sailed 2.5 mi due south, the new bearing was N 25° E. Find the distance between the ship and the lighthouse at each location. 60. Distance across a River Standing on one bank of a river flowing north, Mark notices a tree on the opposite bank at a bearing of 115.45°. Lisa is on the same bank as Mark, but 428.3 m away. She notices that the bearing of the tree is 45.47°. The two banks are parallel. What is the distance across the river? 61. Height of a Balloon A balloonist is directly above a straight road 1.5 mi long that joins two villages. She finds that the town closer to her is at an angle of depression of 35°, and the farther town is at an angle of depression of 31°. How high above the ground is the balloon? 62. Measurement of a Folding Chair A folding chair is to have a seat 12.0 in. deep with angles as shown in the figure. How far down from the seat should the crossing legs be joined? (Find length x in the figure.) 63. Angle Formed by Radii of Gears Three gears are arranged as shown in the figure. Find angle u. 388 3.6 2.7 1.6 u 64. Distance between Atoms Three atoms with atomic radii of 2.0, 3.0, and 4.5 are arranged as shown in the figure. Find the distance between the centers of atoms A and C. 3.0 188 4.5 A B C 2.0 65. Distance between Inaccessible Points To find the distance between a point X and an inaccessible point Z, a line segment XY is constructed. It is found that XY = 960 m, angle XYZ = 43° 30′, and angle YZX = 95° 30′. Find the distance between X and Z to the nearest meter. 66. Height of an Antenna Tower The angle of elevation from the top of a building 45.0 ft high to the top of a nearby antenna tower is 15° 20′. From the base of the building, the angle of elevation of the tower is 29° 30′. Find the height of the tower. 67. Height of a Building A flagpole 95.0 ft tall is on the top of a building. From a point on level ground, the angle of elevation of the top of the flagpole is 35.0°, and the angle of elevation of the bottom of the flagpole is 26.0°. Find the height of the building. 438 309 958 309 960 m Y X Z 45.0 ft 298 309 158 209 318 358 1.5 mi NOT TO SCALE 12.0 in. 54.88 70.48 17.0 in. x
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